Metropolis sampling is a standard method for generating realistic images with global indirect illumination effects. Metropolis sampling is unbiased and adaptive. It is unbiased in the sense that generated results can be shown to be correct on average, which is desirable for predictive rendering applications. It is adaptive in the sense that that the procedure aims to spend most computational effort on parts of the light transport simulation that contribute the most absolute radiance to the final image. However, absolute radiance, where standard Metropolis sampling concentrates its effort, is not necessarily a good measure for adaptive sampling.
The standard Metropolis light transport procedure generates a number of samples (x⊥i,y⊥i,P⊥i) where x and y are image coordinates, and P is a path coordinate vector, a high-dimensional vector that identifies a particular chain of ray segments that propagate light from a light source to a particular pixel of a viewing plane. The Metropolis process generates samples such that they are distributed according to the path throughput function f(x, y, P) that measures the differential contribution of a single light path to a single image-space location. The final image is obtained from the samples by marginalizing over P, i.e., computing the density of the samples over the image. However, the current method may be slow in terms of obtaining visual convergence.